![Cond-Mat.Other] 16 Nov 2004 Ntblt Htapasi Lgtyoiie Metallic Oxidized Slightly Constraint](http://data.docslib.org/img/670714a4af931b95aaf294d4261fc8cf-1.webp)
arXiv:cond-mat/0407773v2 [cond-mat.other] 16 Nov 2004 ntblt htapasi lgtyoiie metallic oxidized slightly constraint. a a in under powder appears that instability ffc ymaso neprmn ihacano metallic of chain a with experiment beads. an of means by effect u ocuin r ie nSc IV. Sec. in D. given III the are and of C conclusions III Our interpretation Secs. in quantitative mechanism followed transition and physics B, conduction III standard qualitative Sec. a a in in ex- results by an our done A present easily III We Sec. be laboratory. in can introduce that we II, periment Sec. in effect coherer swl steiflec feetoantcwvso their on waves electromagnetic of conductance. influence the media, as granular well as as such prop- media thermal non-homogeneous and We of electrical the erties properties. of history collective the the discuss also of instead grains) between inwti h ri sebyas a eninvoked. been has also assembly grain the within tion effect. heating Joule a by lcrsai forces, electrostatic unleettruhtemetal-oxide/semiconductor- the junction, through metal effect tunnel lwrlxtoso eitneas cu ne certain under occur and also fluctuations resistance temporal conditions. of effect); relaxations is Branly volt- slow state threshold DC a conducting (the exceeds a source age to external tran- the state as a insulating observed instance, For an its phenomena. from in Branly other sition E. to produced by related 1890 is is in wave discovered and was electromagnetic effect The an magnitude vicinity. as of orders soon several as by irreversibly falls sistance radw fteoielyr ngrains, on layers oxide electrical the verification: of clear scale a breakdown contact un- without the well invoked at not been processes have are possible still Several they derstood. 1900, wireless near first transmission the in radio involved were media granular metallic lcrclcnutvt ngaua ei n rnyscoh Branly’s and media granular in conductivity Electrical h oee rBal ffc sa lcrclconduction electrical an is effect Branly or coherer The u oli hsppri oudrtn h CBranly DC the understand to is paper this in goal Our lhuhteeeetia rnpr hnmn in phenomena transport electrical these Although 8 u ou so h oa rpris(h contacts (the properties local the on is focus Our 2 oee ffc ai aedtco sdfrtefis wirele elec first an to the conductivity for fillings used metal detector the wave of radio sensitivity a the an – temperature illustrates effect also microcontact coherer experiment the The of thermometer. resistive occ determination microwelding implicit where an grains an volta from between comes external microcontacts transition critical the This low of observed. a is At state conductive media. granular metallic of 9 eso o ipelbrtr xeietcnilsrt ce illustrate can experiment laboratory simple a how show We fe re eiwo h itr fthe of history the of review brief a After 4 .INTRODUCTION I. h trcino risb oeua or molecular by grains of attraction the 5 n oa edn fmicrocontacts of welding local and 4,6,7 1 h nta ihpwe re- powder high initial The lblpoeso percola- of process global A aoaor ePhysique, de Laboratoire M 62 6 l´edIai,6 0 yn France Lyon, 007 69 d’Italie, all´ee 46, 5672, UMR rcFalcon Eric 3 h modified the Dtd coe 5 2018) 25, October (Dated: ∗ 3,5,6 cl oml u´rer eLyon, Sup´erieure de Normale Ecole ´ n enr Castaing Bernard and 1 odr a bevdadetnieysuidb Branly by 1890. studied in extensively and observed was powders nuneo h lcrcrdain rmtesak”the spark;” the from radiations electric the the under of increased conductivity influence powder “the in that discovered the recall was Because (it time value. this high 1897), at known earlier not its was restor- to electron tapped resistance was the tube the ing con- until This remained ohms. state several ductive re- to the reduced away, distance suddenly When was a at sistance surfaces. an generated particle was to spark a the electric due has on an megohms present it many likely tube, layer of ebonite oxide resistance or initial glass high a very in electrodes two tween otiiga nuto oladatb ihfillings. with circuit tube a a and closing coil and induction con- an opening powder containing successively the of by increase ductivity considerable forces, a electromotive observed various and of action the metallic under of Calzecchi- behavior powders T. the on 1884 experiments In performed waves. Onesti hertzian re- of discovery his later, the the and years ter time, 20 convinced, some the not published was were At sults London conductivity. of in indicated Society as tube change Royal distance a sudden a such its at sparks that by electric fact to important sensitive was appears the Hughes discovered waves). have acoustic to tube detect was a to it with designed because and microphone first blocks, (a granules rest- carbon metallic two rod with in carbon filled grooves a the of in formed contact ing Ley- loose a a for of re- nomenon current filings discharge a metal jar. the of den of passage of the mixture increase from a permanent sulting of the conductivity 1835 electrical in observed Munk e f10Mz ol nueacn cosawr loop away. wire meters a few across a arcing gap, small induce a or- could containing the MHz) 100 of of that waves der noticed electromagnetic frequency He (high waves. sparks electromagnetic and generation of H. space propagation by free the performed demonstrated clearly experiments Hertz electromagnetism, of ory h cino eryeetoantcwvso metallic on waves electromagnetic nearby of action The hsdsoeywsatcptdb aypol;P S. P. people; many by anticipated was discovery This n18,sotyatrtepbiaino awl’ the- Maxwell’s of publication the after shortly 1887, In rmgei wave. tromagnetic l rbe,teepaaino Branly’s of explanation the problem, old 15 I RE ITRCLREVIEW HISTORICAL BRIEF A II. e rniinfo nisltn oa to insulating an from transition a ge, 12 lcr-hra opigi h vicinity the in coupling electro-thermal r.Oraprtsalw st obtain to us allows apparatus Our urs. 1 hc saaoost h s fa of use the to analogous is which , rnycle i eiea“ai odco”to conductor” “radio a device his called Branly hnmtli lnsaeloeyarne be- arranged loosely are filings metallic When srdotasiso,adbsdon based and transmission, radio ss n17 .E uhsosre iia phe- similar a observed Hughes E. D. 1879 In ti lcrcltasotproperties transport electrical rtain rr ipeexperiment simple A erer: 13 ogtm af- time long a 10,11 14 2 meaning of the prefix “radio” at this time was “radiant” sualization (with an infrared camera) of the conduction or “radiation.” He performed other experiments with paths when a very high voltage (> 500 V) was applied various powders, lightly or tightly compressed, and found to a monolayer of aluminium beads.6 More recently, the that the same effect occurred for two metallic beads in action at a distance of sparks was investigated.7 For ad- contact, and for two slightly oxidized steel or copper wires ditional information about the history of the coherer, see lying across each other with light pressure.16 This loose Refs. 21 and 22. or imperfect contact was found to be extremely sensitive to a distant electric spark. This discovery caused a considerable stir when O. III. ELECTRICAL CONDUCTIVITY OF A CHAIN OF METALLIC BEADS Lodge in 1894 repeated and extended Hertz’s experi- ments by using a Branly tube, a much more sensitive detector than the wire loop used by Hertz.11,14 Lodge Understanding the electrical conduction transition in improved the Branly tube so that it was a reliable, re- granular materials is a complicated problem that depends producible detector, and automated it by tapping on on many parameters: the statistical distribution of the the tube with a slight mechanical shock. Lodge called shape and size of the grains, the applied force, and the this electromagnetic wave detector a “coherer” from the local properties at the contact scale of two grains, that Latin cohaerere, which means “stick together.” He said is, the degree of oxidization, surface state, and rough- that the fillings “coherered” under the action of the elec- ness. Among the phenomena proposed to explain the tromagnetic wave and needed to be “decoherered” by a coherer effect, it is easy to show that some have only shock. Later, Branly and Lodge focused their fundamen- a secondary contribution. For instance, because the co- tal research on mechanisms of powder conductivity, and herer effect was observed by Branly with a single contact 16 not on practical applications such as wireless communica- between two grains, percolation cannot be the domi- tions. However, based on using the coherer as a wave de- nant mechanism. Moreover, when two beads in contact tector, the first wireless telegraphy communications were are connected in series with a battery, a coherer effect 19 transmitted in 1895 by G. Marconi, and independently is observed at a sufficiently high imposed voltage, in a by A. S. Popov.12,14,17 Popov also used the coherer to way similar to the action at a distance of a spark or an detect atmospheric electrical discharges at a distance. electromagnetic wave. We will reduce the number of pa- Lodge first hypothesized that the metallic grains were rameters, without loss of generality, by focusing on elec- welded together by the action of the voltages that are trical transport within a chain of metallic beads directly induced by electromagnetic waves.14 According to some connected to a DC electrical source. including Lodge,14,18 the grains became dipoles and at- Computer U, I, R tracted each other by electrostatic forces, inducing grains + I to stick together, thus forming conductive chains. A - Force F shock should be enough to break these fragile chains and Displacement x to restore the resistance to its original value. Branly did
Stepper motor 1 N Force Force not believe this hypothesis, and to demonstrate that mo- sensor 0 x tion of the grains was not necessary, he immersed the par- F < 500 N PVC ticles in wax or resin. He also used a column of six steel balls or disks, which were a few centimeters in diameter. FIG. 1: Schematics of experimental setup. Because the coherer effect persisted, he thought that the properties of the dielectric between the grains played an important role. In 1900, Guthe et al. performed sim- ilar experiments with two balls in contact.19 However, A. Experimental setup the invention by de Forest of the triode in 1906, the first vacuum tube (an audion), supplanted the coherer as a The experimental setup is sketched in Fig. 1. It con- receiver, and Branly’s effect sank into oblivion without sists of a chain of 50 identical stainless steel beads,23 being fully understood. each 8mm in diameter, and 0.1 µm in roughness. The In the beginning of the 1960s, a group in Lille became beads are surrounded by an insulating medium of interested in this old problem. They suggested that at- polyvinylchloride (PVC). A static force F 500 N is ap- tractive molecular forces keep the particles in contact plied to the chain of beads by means of a stepper≤ motor, even after the removal of the applied electrostatic field.5 and is measured with a static force sensor. The number In the 1970s, numerous papers considered the conductiv- of motor steps is measured with a counter to determine ity of granular materials for batteries, but they did not x, the total deformation of the chain that is necessary to focus on the electrical conduction transition.20 In 1975, reach a specific force. During a typical experiment, we a group in Grenoble suggested a mechanism of electri- supply a current (10−6 A I 1 A) and simultaneously cal breakdown of the oxide layer on the grain surfaces measure the voltage U, and≤ thus≤ the resistance R = U/I. and investigated the associated 1/f resistance noise.3 In Similar results have been found by repeating the experi- 1997, the conduction transition was observed by direct vi- ment with an applied voltage and measuring I and thus 3
R. The number of beads N between the two electrodes is tween the electrodes. The saturation voltage per contact varied from 1 to 41 by moving the electrode beads within Uc U0/(N + 1) is found to be constant when the num- the chain. The lowest resistance of the entire chain (a few ber≡ of beads N is varied from 1 to 41 and is on the order ohms) is always found to be much higher than that of the of 0.4 V per contact. However, this saturation voltage electrode and the stainless steel bulk material. depends slightly on the bead material (Uc 0.4V for stainless steel beads, 0.2V for bronze beads,≃ and 0.3V for brass beads), but≃ is of the same order of magnitude.8 B. Experimental results 2
6 U 0 The mechanical behavior of the bead chain is found F = 56 N to be in very good agreement with the nonlinear Hertz 4 F = 100 N 3/2 F =220 N 3 law (given by linear elasticity), that is F x . This 3 result leads to an estimate of the typical∝ range of the 1 2 R ~ kΩ - MΩ deformation between two beads as 2 to 20 µm, and of o R ~ few Ω the apparent contact radius, A, of 40 to 200 µm, when F ob 0 ranges from 10 to 500N. 6 The electrical behavior is much more remarkable than 5 5
Voltage (V) 4 4 the mechanical one. Because no particular precautions -2 3
were taken for the beads, an insulating film (oxide or Voltage (V) 5 4 2 contaminant), a few nanometers thick, is likely present -4 1 0 U at the bead-bead contact. When the applied current to 0 1 2 3 max 4 I * R (I ) (V ) -U 0b max the chain is increased, we observe a transition from an -6 0 insulating to a conductive state as shown in Fig. 2. At -1 - 0.5 0 0.5 1 Current I (A) low applied current and fixed force, the voltage-current U-I characteristic is reversible and ohmic (see arrow 1 FIG. 2: Symmetrical characteristics of a chain of N = 13 in Fig. 2) with a high, constant resistance, R0. This re- 4 7 beads for various forces F and for various current cycles in sistance (R0 10 –10 Ω) at low current depends in a ≃ the range −Imax ≤ I ≤ +Imax. (◦, ⋆): I = 0 → 1A → −1A complex way on the applied force and on the contam- → 0, and (♦) I = 0 → 0.5A → −0.5A → −1A → 0. A inant film properties (resistivity and thickness) at the saturation voltage appears for U0 ≃ 5.8 V corrresponding to contact location. The value of R0 is determined by the a saturation voltage per contact U0/(N + 1) ≃ 0.4 V. The slope of the U-I plot at low current. As I is increased inset shows the reversible return trajectories rescaled by R0b. further, the resistance strongly decreases, corresponding Umax ≡ R0b ∗ Imax ≃ 3.5 V. (See text for details.) to a bias U0 independent of I (see arrow 2). As soon as this saturation voltage U0 is reached, the U-I character- istic is irreversible if the current is decreased (see arrow 3). The resistance reached at low decreasing current, R0b C. Qualitative interpretation (the order of 1–10 Ω), depends on the previously applied maximum current, Imax. Note that the nonlinear return Assume a mechanical contact between two metallic trajectory is reversible upon again increasing the current, spheres covered by a thin contaminant film ( few nm). I, and also is symmetrical when the current applied to The interface generally consists of a dilute set∼ of micro- the chain is reversed (see arrows 4 and 5). For different contacts due to the roughness of the bead surface.4 The applied forces F and different values of Imax, we show mean radius, a, of these microcontacts is of the order that the return trajectories depend only on Imax and fol- of magnitude of the bead roughness 0.1 µm, which low the same reverse trajectory when U is plotted versus is much smaller than the apparent Hertz∼ contact radius IR0b (see the inset in Fig. 2). The values of R0b are de- A 100 µm. Figure 3 schematically shows the creation termined by the slopes of the U-I return trajectories at of∼ good electrical contacts by the transformation of this low and decreasing current (see Fig. 2). poorly conductive film. At low applied currents, the high The decrease of the resistance by several orders of mag- value of the contact resistance (kΩ–MΩ) probably comes nitude (from R0 to R0b) is similar to that of the coherer from a complex conduction path found by the electrons effect with powders1 and with a single contact.16,19 Note through the film within the very small size ( 0.1 µm) that after each cycle of the current, the applied force is re- of each microcontact (see light grey zones in Fig.≪ 3). The duced to zero, and we roll the beads along the chain axis electrons damage the film and lead to a “conductive chan- to form new contacts for the next cycle. With this pro- nel”: the crowding of the current lines within these mi- cedure, the fall of the resistance (the coherer or Branly crocontacts generates a thermal gradient in their vicinity effect) and the saturation voltage are always observed if significant Joule heat is produced. The mean radius and are very reproducible. of the microcontacts then strongly increases by several The saturation voltage U0 is independent of the ap- orders of magnitude (for example, from a 0.1 µm to plied force, but depends on the number of beads be- a 10 µm), and thus enhances their conduction≪ (see ∼ 4
Fig. 3). This increase of the radius is responsible for the ( µs) in the contact vicinity. The maximum tempera- ∼ nonlinear behavior of the U-I characteristic (arrow 1 2 ture reached, Tm, is located at the contact, and is related in Fig. 2). At high enough current, this electro-thermal→ to the potential, ϕ, at the isotherm, T , by the Kohlrausch process can lead to local welding of the microcontacts equation4,24 (arrow 2 in Fig. 2); the film is thus pierced in a few Tm ′ ′ ′ places where purely metallic contacts (few Ω) are created ϕ2(T )=2 λ(T )ρ(T )dT , (1) (see the black zones in Fig. 3). (Note that the current- T carrying channels (bridges) are a mixture of metal and Z the film material rather than a pure metal. It is likely where λ(T ) is the thermal conductivity and ρ(T ) is the that the coherer action results in only one bridge – the electrical resistivity of the conductor, both depending on contact resistance is lowered so much that piercing at the temperature T . Thermal equilibrium means that the other points is prevented.) The U-I characteristic is re- heat flux, λ(T )~ T , across the isothermal surfaces, S, is ∇ versible when I is decreased and then increased (arrow due to the electrical power, Iϕ(T ), where ϕ(T ) is the 3 in Fig. 2). The reason is that the microcontacts have potential between one of the conductors and the contact been welded, and therefore their final size does not vary (ϕ(T0) = U/2). This thermal equilibrium, Iϕ(T ) = ± any more for I < Imax. The U-I reverse trajectory then λ~ (T ). dS~, and the current density ~j = ~ (ϕ)/ρ, depends only on the temperature reached in the metallic S − ∇ −∇ thusRR gives ϕdϕ = λρ dT , which leads by integration to bridge and no longer depends on the bridge size as for ∓ the initial trajectory. Eq. (1). For many conductors, the Wiedemann-Franz law states that4 Metal Contaminant/oxide film (few nm) I λρ = LT, (2) Metal − 2A ~ 100 µm where L = π2k2/(3e2) = 2.45 10 8 V2/K2 is the 2a 2ai f Lorentz constant, k is the Boltzmann× constant, and e is the electron charge. If we combine Eqs. (1) and (2) Electrical contact area with ϕ(T0)= U/2, we can express the relation between metallic ( ) ± quasi-metallic ( ) Tm and the applied voltage, U, as + Mechanical contact area 2 + + Apparent contact area U T 2 T 2 = . (3) m − 0 4L R ~ kΩ - MΩ R ~ Ω Equation (3) shows that the maximum temperature T Diameter 2a 2a m f reached at the contact is independent of the contact ge- ometry and of the materials in contact because both the 2a Increasing current i electrical resistivity, ρ(T ), and the thermal conductivity, λ(T ), are due to the conduction electrons, which leads to FIG. 3: Schematic of the electrical contact creation through the temperature dependence given by Eq. (2). microcontacts by transformation of the poorly conductive A voltage near 0.4V across a contact leads, from Eq. (3) and the value of L, to a contact temperature contaminant/oxide film. At low current I, the electrical con- ◦ ◦ tact is mostly driven by a complex conduction mechanism near 1050 C (Tm = 1320K) for a bulk temperature 20 C through this film via conductive channels (of areas increas- (T0 = 290K). A voltage U 0.3–0.4 V thus leads from ing with I). At high enough I, an electro-thermal coupling Eq. (3) to contact temperatures≃ that exceed the melting generates a welding of the microcontacts leading to efficient point of most conducting materials. Efficient metallic conductive metallic bridges (of constant area). bridges are therefore created by microwelding. Beyond the quantitative agreement with the experimental satu- ration voltage Uc (see Sec. IIIB and Fig. 2), Eq. (3) also explains why Uc is the relevant parameter in the experi- D. Quantitative interpretation ments in Sec. III B, and not the magnitude of the current. In addition, when U approaches Uc (see Fig. 2), the lo- We now check the interpretation in Sec. III C quantita- cal heating of the microcontacts is enough, from Eq. (3), tively. Assume a microcontact between two clean metal- to melt them. Then their contact areas increase, thus lic conductors (thermally insulated at the uniform tem- leading to a decrease of the local resistance. When Uc perature T0, with no contaminant or tarnish film on their is reached, the microcontacts are welded, thus stabilizing surfaces). Such a clean microcontact is called a “spot.” If the contact areas, the voltage, and the contact temper- an electrical current flowing through this spot is enough atures. The phenomenon is therefore self-regulated in to produce Joule heating (assumed to be totally dissi- voltage and temperature. pated by thermal conduction in the conductors), then a Our quantitative model describes only the electrical steady-state temperature distribution is quickly reached behavior of a welded contact, that is, when the saturation 5 voltage is reached. It describes the reversible U-I reverse of the contact or on the metal used for the contact. How- trajectory (when this contact is cooled by decreasing the ever, for alloys the right-hand side of Eq. (8) depends on current from Imax, then eventually reheated by increasing α, the temperature coefficient of the electrical resistivity I.) The contact area is assumed to be constant because of the alloy. This additional parameter is related to the the contact has been welded, and I < Imax. presence of defects in the material. The normalized U-I Let us derive the analytical expression of the nonlinear reverse trajectory (that is, U as a function of IR0b in the U-I reverse trajectory.8 We introduce the “cold” contact inset of Fig. 2) are compared in Fig. 4 with the theoretical resistance R0b present at currents sufficiently low so as solutions, Eq. (8), for pure metals and for a stainless steel to not cause any appreciable rise in the temperature at alloy. Very good agreement is found between the experi- the contact. The bulk conductor is at the room temper- mental results and the electro-thermal theory, especially ature T0, with an electrical resistivity ρ0 = ρ(T0). The for the alloy. Qualitatively, the alloy solution is closer to derivation of R0b involves the same equipotential surfaces the experimental data than the solution for a pure metal. during a change between the “cold” state (denoted by a The agreement is even quantitatively excellent (see the star) ϕ⋆, and the “hot” state ϕ(T ): the same current thus solid line in Fig. 4). For this comparison, the value α−1 −1 involves the same current density in both states, and thus is equal to 4T0 instead of 3.46T0 (the α value for AISI ⋆ 26 −1 ~ (ϕ )/ρ0 = ~ (ϕ)/ρ(T ). Note that an equipotential also 304 stainless steel), because the value of α for the is∇ an isothermal.∇ At thermal equilibrium, this equation bead material (AISI 420 stainless steel) is unknown, but and the differential expression of Eq. (1) give should be close to 3.46T0. During the experimental re- verse trajectory, the equilibrium temperature, Tm, of a dϕ⋆ dϕ λ(T ) microcontact also is deduced from Eq. (7) with no ad- = = dT. (4) ρ0 ρ(T ) ∓ϕ(T ) justable parameters (see the inset in Fig. 4). Therefore, when the saturation voltage is reached (U0 =5.8 V), Tm ◦ We use Ohm’s law and integrate Eq. (4) between the is close to 1050 C which is enough to soften or melt the 24 isothermal surfaces T0 and Tm and find microcontacts between the N = 13 beads of the chain. We could say that our implicit measurement of the maxi- Tm IR0b λ(T ) mum temperature (based on the temperature dependence =2 dT. (5) of the material conductivities) is equivalent to the use of ρ0 T0 ϕ(T ) Z a resistive thermometer. The factor of two arises from heat flowing in parallel on both sides of the contact whereas the current uses these both sides in series. The temperature dependence of the thermal conductivity, λ(T ), and electrical conductivity, 6 ρ(T ), of the material in contact is given by Eq. (2) and U 0
ρ(T )= ρ0[1 + α(T T0)], (6) − 5 where α is the temperature coefficient of the electrical resistivity. 4 Equations (2) and (6) let us find explicit expressions for
λ(T ) and ϕ(T ) which can be substituted in Eq. (5). The 3 6 U
U (V) 0 reverse trajectory IR0b depends only on the temperature 5 Tm (that is, on U), 2 4
3 U (V) 2 2 2 U 1 Tm = T + , (7) 1 T (oC) 0 2 m s 4L(N + 1) 0 0 300 600 900 1200 0 and finally gives (see the Appendix in Ref. 8 for the de- 0 1 2 3 U 4 I * R (V) max tails) 0b
√L θ0 cos θ FIG. 4: Comparison between the experimental U-I reverse IR0b = 2(N + 1) − dθ, trajectories of Fig. 2 (symbols) and theoretical curves from α [1 + (αT ) 1]cos θ + cos θ −1 0 0 0 Eq. (8) for an alloy with stainless steel properties [α = 4T0 Z −1 (8) (−) or 3.46T0 (· · · )], and for a pure metal [α = T0 (−.−)]. where θ0 arccos(T0/T ) and N + 1 is the number ≡ m The inset shows the theoretical maximum temperature, Tm, of contacts in series in the chain. Note that only R0b from Eq. (7), reached for one contact when the chain of N = depends on the contact geometry, and its value is easily 13 stainless steel beads is submitted to a voltage U. determined experimentally (see Sec. III B). −1 25 Because for pure metals (α T0), the right-hand side of Eq. (8) does not depend explicitly≃ on the geometry 6
IV. CONCLUSIONS microwelding of contacts (even for a voltage as low as 0.4V). Based on this self-regulated temperature mecha- Electrical phenomena in granular materials related to nism, an analytical expression for the nonlinear U-I re- the electrical conduction transition such as the Branly verse trajectory was derived, and was found to be in good effect have been interpreted in many different ways but agreement with the data. The theory also allows for the without a clear demonstration. We have reported the determination of the microcontact temperature through observation of electrical transport through a chain of ox- the reverse trajectory with no adjustable parameters. We idized metallic beads under an applied static force. A could attempt to directly visualize this process with a mi- transition from an insulating to a conducting state is croscope or infrared camera. But for this purpose a very observed as the applied current is increased. The U-I powerful electrical source must be applied, far in excess characteristics are nonlinear, hysteretic, and saturate to of that necessary to produce true coherer phenomena (see a low voltage per contact ( 0.4 V). From this simple ex- for example Ref. 6). periment, we have shown that≃ the transition triggered by the saturation voltage arises from an electro-thermal cou- pling in the vicinity of the microcontacts between each Acknowledgments bead. The current flowing through these spots generates local heating which leads to an increase of their contact We thank D. Bouraya for the realization of the ex- areas, and thus enhances their conduction. This current- perimental setup, and Madame M. Tournon-Branly, the induced temperature rise (up to 1050◦C) results in the granddaughter of E. Branly, for discussions.
∗ Electronic address: [email protected]; less telegraphy,” The Electrician, May 5, 40–41 (1899), URL: http://perso.ens-lyon.fr/eric.falcon/
24 J. A. Greenwood and J. B. P. Williamson, “Electrical (CRC Press, 1981), 60th ed. conduction in solids. II. Theory of temperature-dependent 26 Stainless Steel AISI 304 specifications at CERN, conductors,” Proc. Roy. Soc. A 246, 13–31 (1958).